And c-sections raised the chance of an ectopic pregnancy by 9%, according to a study of more than 800,000 Danish first-time mothers.
Prof Louise Kenny of University College Cork described the risks as “very low”.
Performing 3,000 caesareans would lead to one extra stillbirth in a subsequent pregnancy, she said.
“Although these are rare outcomes, they are devastating for parents and healthcare providers,” Prof Kenny told BBC News.
“Therefore, we would advise women to avoid requesting a caesarean section when there is no medical indication to do so.”
Dr Patrick O’Brien of the Royal College of Obstetricians and Gynaecologists said the findings were “reassuring”.
“It’s quite reassuring that any increased risk of stillbirth in a subsequent pregnancy is very small indeed,” he said.
“Any stillbirth is a stillbirth too many but the absolute risk is very small indeed.”
The study, published in PLOS Medicine, is one of the largest so far to look at links between c-sections and stillbirth.
The study analysed data from 832,996 women from Danish national registers.
There are about 4,000 stillbirths every year in the UK and one in 200 pregnancies ends in stillbirth.
An ectopic pregnancy happens when a fertilised egg implants itself outside of the womb, usually in one of the fallopian tubes.